To touch back on the shitloads you describe, yes there may be something along those lines. I imagine then that they would have to be looked at tin the same way as a common law relationship is. Which most of the time is no different than married. The added cost of a new address would negate the gains these people may be trying to grab.
On the other hand, we wouldn't want to falsely categorize otherwise unrelated people living at the same address (e.g. roommates) as "partners" and reduce their UBI, right? This gets very complicated very quickly.
Overall the main thing making me extremely skeptical towards UBI is that it is loved both by bright-red socialists and hardcode libertarians, which seems to indicate that the idea is unworkable in practice. It won't improve social fairness and it won't eliminate the state's responsibility for welfare, or achieve whatever other goals those groups might ascribe to UBI. In practice this would be a welfare system under a different name, with a bunch of exceptions and limitations and lots and lots of regulation.
Or we could focus on what has been working reasonably well if not perfectly, e.g. improving education, healthcare, public safety, infrastructure, etc to give people a better chance at upward mobility plus a decent safety net, boring as it may be.